Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 7 x^{2} - 3 x - 4}{- 3 x^{2} + 5 x - 9}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 2 times gives: LaTeX: \lim_{x \to \infty}\frac{- 7 x^{2} - 3 x - 4}{- 3 x^{2} + 5 x - 9} = \lim_{x \to \infty}\frac{- 14 x - 3}{5 - 6 x} = \lim_{x \to \infty}\frac{-14}{-6} = \frac{7}{3}